The Optimal Funnel

While at IKEA a while ago, we purchased two "CHARM" funnels for very cheap. It seems that you get what you pay for.

As you can see, the slope of the funnel wall approaches zero as you reach the bottom hole. This means that the stuff you are trying to get to drain down the hole is essentially heading sideways, and must change direction very significantly in order to fall directly down the hole.

This fairly idiotic funnel design got me thinking: What is the optimal curve for a funnel's walls? Unfortunately, I've been incredibly busy recently, and have not had a chance to really work on this problem myself. However, this is an opportunity for another Lansey Brothers' Blog Contest! I am interested to find out what you, dear reader, think is the optimal curve. In some way, it should be a function of D (diameter of mouth), d (diameter of spout), and h (height of funnel), which should probably be order D, and where clearly d<D.

So if people can work this, and email me their solutions (MS Word or PDF form, with a copyright to themselves on it), I'll make a post in the future with a summary of the solutions, and my favorite. Please email solutions to .